# How far away is it?

1. Nov 18, 2011

### PatrickPowers

Sorry to ask such a basic question, but I can't seem to figure it out.

On earth a device is made that can measure the distance to a star one light year away. Now suppose the device is coincidental with the earth and has already been accelerated to 0.5c. What distance will it measure now?

It can use radar and bounce a pulse off the star, measure the time delay and blue shift, and do a calculation to determine how far away the star was when the pulse was sent. But this is beyond me. I can't even tell whether the star would be measured as less than one light year, more, or the same.

2. Nov 18, 2011

### HallsofIvy

Staff Emeritus
Are you asking: If an object that can measure the distance (at distance 1ly in earth's frame of reference) to a star measures that distance as it passses the earth at 0.5c, what distance will it measure? I would think that would be just the Lorentz contraction:
$$\sqrt{1- .5^2}= \frac{\sqrt{3}}{2}$$